25 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
9171 | The function of names is simply to refer [Kripke] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |